We found that \(\operatorname{Eig}(V)\)  provides a framework suitable for any non-degenerate finite-dimensional Hamiltonian, including non-Hermitian Hamiltonians in particular. However, this brings us to the question how the theory of Hermitian systems relates to \(\operatorname{Eig}(V)\) . The geometric framework for such Hermitian cases was pioneered by Aharonov and Anandan in [1]} (see also the elaboration in [2]}). The geometric spaces found there differ significantly from the spaces obtained here. Nevertheless, we will show that they can be obtained from \(\operatorname{Eig}(V)\) .
